Choosing an optimal switching moment on the financial market with alternative strategies (semimartingale approach)

Yu. S. Mishura, Ya. A. Ol'tsik

National Taras Shevchenko University of Kyiv, Faculty of Mechanics and Mathematics

Abstract: Let the investor operate with bonds and stocks on the financial market. We fix the interval $[0,T]$ and suppose that once during this period of time the investor is able to choose between two alternative portfolios or, in other words, to switch his strategy. It is assumed that both portfolios are governed by linear stochastic differential equations. We look for an optimal switching moment using the theory of “turning” stopping times.

Keywords: stochastic process, optimal stopping time, linear stochastic differential equation, investor, capital.

Received: 25.03.1998

DOI: 10.4213/tvp482

 English version: Theory of Probability and its Applications, 2001, 45:3, 480–493

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